Finite Group Databasebeta

← #29748675

Subgroups — #29748675

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450364C211yesmaximal, characteristic, complemented
2#21448889C211yesmaximal, characteristic
3#21447207C211yesmaximal, characteristic
4#21447058C211yesmaximal, characteristic
5#21447058C211yesmaximal, characteristic
6#21446496C211yesmaximal, characteristic, complemented
7#21446458C211yesmaximal, characteristic, complemented
8#21446409C211yesmaximal, characteristic, complemented
9#21446389C211yesmaximal, characteristic, complemented
10#21446379C211yesmaximal, characteristic, complemented
11#21446076C211yesmaximal, characteristic, complemented
12#21446068C211yesmaximal, characteristic
13#21445831C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic
15C61×#2073C211yesmaximal, characteristic
16C2×#14519764C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839703—21no—
30#16839703—21no—
31#16839667C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839659—21no—
35#16839658C2211yescharacteristic
36#16839658C2211yescharacteristic
37#16839656—21no—
38#16839650—21no—
39#16839647—21no—
40#16839634—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758196C2211yescharacteristic
44C22⋊C4×Dic61—21no—
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#382C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C23×Dic61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519764—22no—
64#14519764—22no—
65C4×Dic122—22no—
66C4×Dic122—41no—
67D4×Dic61—22no—
68D4×Dic61—41no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196D411yescharacteristic
78C2×#11758196D411yescharacteristic
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87#14519711—22no—
88#14519710—22no—
89C4⋊#92418—41no—
90#14519702—22no—
91#14519702—41no—
92#14519700—22no—
93#14519700—22no—
94#14519698—22no—
95#14519698—41no—
96C8×Dic61—41no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107C22×D4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C42×C61C2311yescharacteristic
116#102×C61—22no—
117#102×C61—22no—
118#95×C61—21no—
119#95×C61—21no—
120C24×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61#4112yes—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61—81no—
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122#4112yes—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C22⋊C4×C61—42no—
163C22⋊C4×C61—81no—
164C42×C61—21no—
165C42×C61—21no—
166C22⋊Dic61—24no—
167C22⋊Dic61—24no—
168C22⋊Dic61—42no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—42no—
174C4⋊Dic61#4112yes—
175C4⋊Dic61#4112yes—
176#11758196—22no—
177#11758196—41no—
178#11758196—42no—
179#11758196—42no—
180#11758196—81no—
181#11758196—81no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—42no—
187C4×Dic61—81no—
188C4×Dic61—81no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C23×C61—22no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61C22×D411yescharacteristic
203D4×C61—22no—
204D4×C61—22no—
205D4×C61—41no—
206D4×C61—41no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×C4×C61H(5,𝔽2)11yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—22no—
233C2×Dic61—21no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—84no—
252C2×Dic61#13512yes—
253Dic122—22no—
254Dic122—22no—
255Dic122—41no—
256Dic122—41no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—41no—
260#92418—41no—
261#26762—611nomaximal, Sylow
262C22×C61—42no—
263C22×C61—42no—
264C22×C61—42no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61#52511yescharacteristic
270C22×C61#54611yescharacteristic
271C22×C61#54811yescharacteristic
272C22×C61C2×#13511yescharacteristic
273C22×C61#57511yescharacteristic
274C22×C61#57611yescharacteristic
275C22×C61#57811yescharacteristic
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61#52911yescharacteristic
282C4×C61#53911yescharacteristic
283C4×C61#55211yescharacteristic
284C4×C61#55311yescharacteristic
285Dic61—22no—
286Dic61—41no—
287Dic61—42no—
288Dic61—41no—
289Dic61—42no—
290Dic61—42no—
291Dic61—41no—
292Dic61—81no—
293#2509—611no—
294#2367—611no—
295#2073D6111yescharacteristic
296#2067—611no—
297#2042—611no—
298#2042—611no—
299#1933—611no—
300#1928—611no—
301#1921—611no—
302#1918—611no—
303#1916—611no—
304#1863—611no—
305#1862—611no—
306#1805—611no—
307C4×#102—611no—
308C2×C61—82no—
309C2×C61#246011yescharacteristic
310C2×C61#310211yescharacteristic
311C2×C61#312411yescharacteristic
312C2×C61#329711yescharacteristic
313C2×C61#331311yescharacteristic
314C2×C61#336411yescharacteristic
315C2×C61#337011yescharacteristic
316C2×#124—611no—
317C2×C4×Q8—611no—
318C2×C4×D4—611no—
319C2×#107—611no—
320C2×#107—611no—
321C2×C4⋊C8—611no—
322C2×#103—611no—
323C2×#103—611no—
324C2×#103—611no—
325C2×#103—611no—
326C2×#102—611no—
327C2×#102—611no—
328C2×#102C2×D6111yescharacteristic
329C2×#102C2×D6111yescharacteristic
330C2×C4×C8—611no—
331#400—1221no—
332#400—1221no—
333#391—611no—
334#390C2×D6111yescharacteristic
335#389—611no—
336#389—611no—
337#389—611no—
338#389—611no—
339#389—1221no—
340#388—1221no—
341#388—1221no—
342#387—1221no—
343#385—1221no—
344#382C2×D6111yescharacteristic
345C4×C4⋊C4—611no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4—611no—
348C4×C22⋊C4—1221no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340C2×D6111yescharacteristic
354#340C2×D6111yescharacteristic
355#336—611no—
356#336—611no—
357#336—611no—
358#336C2×D6111yescharacteristic
359C61#2676211yescharacteristic, complemented, Sylow
360C22×Q8—611no—
361C22×D4C22×D6111yescharacteristic
362C23×C4—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8C22×D6111yescharacteristic
366C22×C8C22×D6111yescharacteristic
367#124—1222no—
368#124—1222no—
369C4×Q8—1222no—
370C4×Q8—2441no—
371C4×D4—1222no—
372C4×D4—2441no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—1221no—
394C2×C42—1221no—
395C2×C42—1221no—
396C2×C42C22×D6111yescharacteristic
397#107—1222no—
398#107—1222no—
399C4⋊C8—2441no—
400#103—1222no—
401#103—1222no—
402#103—1222no—
403#103—2441no—
404#102—22no—
405#102—22no—
406#102—1222no—
407#102—2441no—
408C4×C8—2441no—
409#95—21no—
410#95—21no—
411#95—611no—
412#95—611no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421C24—21no—
422C2×Q8—612no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4#1175822412yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—4881no—
446C22×C4—2442no—
447C22×C4—2442no—
448C22×C4D4×D6111yescharacteristic
449C22×C4D4×D6111yescharacteristic
450C22×C4C23×D6111yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—612no—
470C4⋊C4—612no—
471C4⋊C4—1222no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—4881no—
477C4⋊C4—4881no—
478C4⋊C4—2441no—
479C4⋊C4—2442no—
480C4⋊C4—2442no—
481C4⋊C4—2442no—
482C22⋊C4—42no—
483C22⋊C4—81no—
484C22⋊C4—1224no—
485C22⋊C4—1224no—
486C22⋊C4—2442no—
487C42—21no—
488C42—21no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42—4881no—
494C42—4881no—
495C42—2442no—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C2×D4×D6111yescharacteristic
504Q8—1222no—
505Q8—1222no—
506Q8—2441no—
507Q8—2441no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—612no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1222no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—4884no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4#41×D6111yescharacteristic
553C2×C4#41×D6111yescharacteristic
554C2×C4#41×D6111yescharacteristic
555C2×C4C2×#1175822411yescharacteristic
556C2×C4#1451982311yescharacteristic
557C2×C4#1451982411yescharacteristic
558C8—41no—
559C8—41no—
560C8—2441no—
561C8—2441no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1684027211yescharacteristic
570C22#1684040411yescharacteristic
571C22#1684042011yescharacteristic
572C22#135×D6111yescharacteristic
573C22#1684055811yescharacteristic
574C22#1684056611yescharacteristic
575C22#1684057611yescharacteristic
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—1222no—
582C4—4881no—
583C4—2442no—
584C4—2442no—
585C4—2442no—
586C4—2441no—
587C4—2441no—
588C4—2441no—
589C4#1684028911yescharacteristic
590C4#1684035611yescharacteristic
591C4#1684044811yescharacteristic
592C4#1684046311yescharacteristic
593C2—82no—
594C2#2144977211yescharacteristic
595C2#2145583411yescharacteristic
596C2#2145607811yescharacteristic
597C2#2145767211yescharacteristic
598C2#2145788811yescharacteristic
599C2#2145850111yescharacteristic
600C2#2145856711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2073C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2073D61
hypocenterC61#26762
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21450364C2semidirect
6. #21446496C2semidirect
7. #21446458C2semidirect
8. #21446409C2semidirect
9. #21446389C2semidirect
10. #21446379C2semidirect
11. #21446076C2semidirect
13. #21445831C2semidirect
359. C61#26762semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214503642
#214488892
#214472072
#214470582
#214464962
#214464582
#214464092
#214463892
#214463792
#214460762
#214460682
#214458312
#102×Dic612
C61×#20732
#2676261